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Theorem eqnetri 2222
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
eqnetr.1 A = B
eqnetr.2 B𝐶
Assertion
Ref Expression
eqnetri A𝐶

Proof of Theorem eqnetri
StepHypRef Expression
1 eqnetr.2 . 2 B𝐶
2 eqnetr.1 . . 3 A = B
32neeq1i 2215 . 2 (A𝐶B𝐶)
41, 3mpbir 134 1 A𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-ne 2203
This theorem is referenced by:  eqnetrri  2224  2on0  5949  1n0  5955
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